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Abstract
The plasmonic interconnect circuit (PIC) has shown great application prospects in chip-level optoelectronic systems. In this paper, we focus on a class of on-chip PIC based on a subwavelength metal grating coupler and decoupler. We systematically study the effect of grating depth on the coupling and decoupling efficiency of the designed device. The energy utilization of the device can be greatly improved and the device footprint has been reduced by about 30% at the same time by using an index matching layer. The optimal operating point of the device is finally stabilized around 1310 nm by adjusting the refractive index of the top matching layer and introducing the bottom metal reflector. The coupling and decoupling efficiency of the optimized device can reach 38% and 18% respectively and can be future adjusted linearly and synchronously by changing the refractive index of the matching layer. Our work provides an efficient and easily-fabricated PIC platform and gives the possibility to realize tunable on-chip plasmonic interconnection.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Optoelectronic integrated circuits (OEICs) that can provide large bandwidth and low interconnect delay are considered to be one of the effective ways to break through the bottleneck of gradual failure of Moore's Law in electronic circuits [1]. However, due to the limitation of optical diffraction limit, the feature sizes of the optical devices based on dielectric materials are about 1 µm which has a big gap with the scale of electronic devices (∼10 nm), it is difficult to achieve their integration in the same circuit loop [2]. Therefore, it is necessary to develop optical devices with scales smaller than the optical diffraction limit for optical information processing [3,4]. Surface plasmon polaritons (SPPs) are electromagnetic waves arise from the coupling between light and collective oscillation of free electrons which enable light to propagate beyond the diffraction limit [5,6]. Plasmonic interconnect circuit (PIC) based on SPPs as information carrier are expected to combine the compactness of an electronic circuit with the bandwidth of a photonic network [7,8].
Previously, SPPs has been widely used in on-chip lasing source [9–11], electro-optical modulators [12–18] and detectors [19–22] as discrete components or combinations for improving the performance of optoelectronic interconnect devices. Recently, researchers have focused on combining various active and passive plasmonic modules to build a complete PIC to achieve high-efficient and compact on-chip signal processing which shows high application prospects in optical communication and monolithic optoelectronic integration [1,23–30]. Throughout these reported cases of PIC, we can find that a complete PIC always consists of three key components: a coupler to connect SPPs with excitation source, a waveguide to transport SPPs and a detector decouples the SPPs into the photonic or electronic signal. The above process includes the photon/electron-SPPs-photon/electron energy conversion form. It is clear that the energy loss generated in this process is an important factor restricting the performance of the PIC. For example, similar to the grating coupler commonly used in Si-based optoelectronics [31], subwavelength periodic metal gratings are often used as coupling structure in PIC. However, in order to obtain above 50% coupling efficiency, shallowed-etched gratings are usually required [12,32]. Compared with lift-off process, metal ion etching process is more complex and costly. On the other hand, shallowed-etched gratings cannot realize SPPs-electron conversion at the decoupling structure of PIC because photons cannot be effectively scattered into the semiconductor substrate [33–36]. In this case, additional etching process is unavoidable. Therefore, it is of great significance to develop both efficient and “ench-free” PIC. In addition, although the center wavelength of the subwavelength metal grating structure can be adjusted by changing the grating period, but the center wavelength is fixed after the device fabrication process. Phase change materials (PCMs) such as liquid crystal [37–39]and electro-optical materials [12,40] whose refractive index can be dramatic changed offer the possibility to dynamically tune the working properties of PIC [41,42].
In this paper, we first focus on the periodic metal grating coupler which can be easily fabricated by lift-off process. Through numerical simulation, we compared the Au-air and Au-PMMA grating coupler on the Ge substrate in order to meet the application in the near-infrared communication band. By adding a high refractive index layer (nPMMA≈1.5) over the metal, we can reduce the original size of Au-air grating coupler by about 30%, at the same time, the scattering loss of SPPs on the Au waveguides can be significantly reduced in the small longitudinal range which is beneficial to obtain more effective energy at the decoupler of PIC. On this basis, though adding a bottom metal reflector and adjusting the refractive index of the matching layer, the coupling and decoupling efficiency of the device are greatly and synchronously improved to over 38% and 18% respectively without changing any structural parameters of the device. Our work provides a tunable, efficient and easily-fabricated PIC platform for further on-chip OEICs.
2. Method
The numerical simulations in this work were carried out via finite-difference time-domain (FDTD) method. The simulation is two-dimensional (2D) because the model is symmetric in the y-direction. The structure is surrounded by air (nair = 1), and the temperature is 300 K. The simulation time is set to 1000 fs. The overall mesh size is 5 nm×5 nm and the mesh accuracy is 4. We use the finer mesh (1 nm×1 nm) on local fine structures to improve simulation accuracy. In the simulation unit cell, the perfectly matched layer (PML) boundary condition is used in both the x direction and the z direction. The incident total-field-scattered-field (TFSF) source (TM-polarization) illuminates the coupling gratings vertically from the top side of the structure. The power monitors placed at different locations are used to calculate the coupling and decoupling efficiency of the device. A power analysis group is used to collect the absorption distribution in the Ge layer. The optical properties of Au and Ge used in the model were taken from the data by Johnson and Palik et al. [43,44].
3. Results and discussion
3.1 Efficient periodic metal grating coupler with the index matching layer
The complete configuration and working process of the PIC device involved in this paper have been discussed in detail in our previous work [34]. This paper aims to further optimize the efficiency of this PIC configuration and explore a simple and convenient way to adjust the device operating characteristics. In order to exclude the interference of other structures in the PIC, we first study the SPPs grating coupler separately. The schematic diagram of the basic Au-air SPPs grating coupler in x-z plane is shown in Fig. 1(a), SPPs can be excited by the grating coupler (red dotted border) under the incident light (red straight arrow) and propagate along the waveguide at Au-air interface. As a SPPs excitation structure, the coupling gratings are used to compensate the wave vector mismatch between the SPPs and the incident light. The coupling condition can be expressed as [6]:
Fig. 1. (a) Schematic diagram of Au-air SPPs grating coupler on the Ge substrate in x-z plane. SPPs can be excited at the area of periodic coupling gratings (red dotted border) under the incident light (red straight arrow) and propagate along the waveguide beside the coupling gratings. (b) Normalized electric field distribution of the Au-air SPPs grating coupler with depth of 200 nm under illumination by 1310 nm TFSF source. (c) Coupling efficiency as a function of different depth of the coupling gratings in the 1100–1500 nm wavelength range.
Figure 1(b) shows the the normalized electric field intensity distribution |Ez| of the basic Au-air SPPs grating coupler (T = 200 nm) at 1310 nm wavelength in the x-z plane. It is obvious that the SPPs can be efficiently excited by the designed grating coupler and propagate symmetrically along both sides of the waveguide. We can find that there is less SPPs field leaking into the Ge substrate due to the larger depth of coupling gratings which will be beneficial to reduce the ‘residual’ photocurrent of the detector of PIC [34–36]. Most of the electric field is concentrated in the air layer above the metal gratings and decays exponentially along the positive z direction, a 1500 nm long power monitor is sufficient to contain most of the SPPs field and in fact only the SPPs propagating close to the waveguide can be effectively utilized by the decoupling gratings of the PIC which will be discussed in the later section. Fixing other parameters of the Au-air SPPs grating coupler, we scanned the coupling efficiency with different grating depths ranging from 0 nm to 400 nm as shown in Fig. 1(c), the designed Au-air SPPs grating coupler can have the coupling efficiency of about 20% when the grating depth is 200–250 nm at 1310 nm wavelength and it is clear that shallower and deeper grating depth is unfavorable for efficient SPPs coupling.
According to Eq. (1), it is feasible to reduce the period (P) of the SPPs grating coupler by increasing the refractive index of the medium above the metal. As shown in Fig. 2(a), we choose polymethylmethacrylate (PMMA) which can be prepared by the simple spin-coating process and has high refractive index (nPMMA ≈ 1.5) as the refractive index matching layer with the thickness of 600 nm. Figure 2(b) shows the the normalized electric field intensity distribution |Ez| of the Au-PMMA SPPs grating coupler (T = 200 nm) at 1310 nm wavelength in the x-z plane. The P and W of the coupled gratings can be reduced to 900 nm and 450 nm respectively, so, the size of the entire Au-PMMA coupler is about 30% smaller than that of Au-air coupler as can be seen from the x-coordinate in Fig. 1(b) and Fig. 2(b). The size of the device can be further reduced by using a higher refractive index matching layer according to Eq. (1). This method of reducing device footprint is universal and suitable for various SPPs interconnect platforms based on grating coupler and decoupler [12,27,28]. Different from the Au-air coupler, the SPPs field can be better confined in the PMMA layer with high refractive index which is of great help to the effective utilization of SPPs energy, although Fig. 2(c) shows a slight decrease in coupling efficiency (about 18% when the grating depth is 150–200 nm) compared to the Au-air coupler because of the higher reflectivity of PMMA layer (See Fig. S1 in Supplement 1).
Fig. 2. (a) Schematic diagram of Au-PMMA SPPs grating coupler on the Ge substrate in x-z plane. (b) Normalized electric field distribution of the Au-PMMA SPPs grating coupler with depth of 200 nm under illumination by 1310 nm TFSF source. (c) Coupling efficiency as a function of different depth of the coupling gratings in the 1100–1500 nm wavelength range.
In order to further reveal the effect of the refractive index matching layer on the propagation of SPPs on the waveguide, we indicate the coupling efficiency as a function of waveguide length (L) in Fig. 3(a-b) and the grating depth of the Au-air and Au-PMMA coupler are all 200 nm. We know that SPPs signals experience large ohmic and scattering losses on the Au-air interface [27,28], although the Au-air coupler can achieve more than 20% coupling efficiency as shown in Fig. 1(c), it is clear that a considerable portion of the SPPs field which cannot be effectively utilized will be scattered into free space, in other words, the ineffective coupling efficiency accounts for a large proportion of the 20%. Therefore, we reduced the length of the power monitor to 500 nm as shown by the blue bidirectional arrow in Fig. 3(c) which only covers the SPPs field near the Au waveguide. In this case, the coupling efficiency of the Au-air coupler decays from 20% to less than 8% just at L = 1 µm, when the SPPs continues to propagate for 20 µm, the coupling efficiency drops sharply to below 5% as shown in Fig. 3(a). Different from the SPPs field distribution that almost traverses the air layer above the waveguide in Fig. 3(c), the SPPs field is better confined in the PMMA layer with higher refractive index as shown in Fig. 3(d). So even using a smaller power monitor, the coupling efficiency of the Au-PMMA coupler at L = 1 µm only drops from 18% to 15% and still remains around 8% at L = 21 µm although the high-refractive-index layer caused some destructive interference of back-reflection as shown in Fig. 3(b&d) [1,30]. Therefore, the PMMA layer can significantly reduce the scattering loss during SPPs propagation. In addition, it should be pointed out that the unidirectional coupling efficiency can be further improved when an asymmetric grating coupler design is adopted [35,45,46], in this paper, taking into account the actual fabrication complexity, only the basic and symmetrical grating coupler is discussed for the convenience of comparative analysis and structural parameter adjustment.
Fig. 3. (a-b) Coupling efficiency of the (a) Au-air grating coupler and (b) Au-PMMA grating coupler with a depth of 200 nm as a function of different waveguide length in the 1100–1500 nm wavelength range with small power monitor. (c-d) Normalized electric field distribution at the (a) Au-air waveguide and (b) Au-PMMA waveguide with coupling grating depth of 200 nm at1310 nm wavelength.
3.2 Tunable and efficient PIC with index matching layer and metal reflector
As described above, the grating depth of about 200 nm can make both the Au-air and Au-PMMA SPPs coupler obtain the high coupling efficiency. However, the higher grating depth is not conducive to the effective decoupling of SPPs at the grating decoupler of the PIC [33]. That is to say, the SPPs excited by the grating coupler cannot be efficiently utilized by the decoupling grating and finally reflected in the improvement of the photocurrent of the actual devices. To resolve this contradiction, on the basis of the above Au-PMMA grating coupler, we add an Au reflector to the Ge substrate. The schematic diagram of the complete PIC is shown in Fig. 4(a). The structural parameters of the Au-PMMA coupler are the same as Fig. 2 (P = 900 nm, W = 450 nm) and the waveguide length is fixed at 6 µm. As for the grating decoupler, while the smaller grating period and duty cycle facilitates the SPPs power flow into the substrate [33], however, we set the period (p) and width (w) of the decoupling gratings to be 700 nm and 350 nm respectively due to the fabrication limitations. As a comparison, we scale up the structural parameters (p = 1000 nm, w = 500 nm) of the PIC based on Au-air. As shown in Fig. 4(a), the distance between the Au reflector and the interface of the grating and Ge substrate is set as t1 = 42 nm, and the thickness (t2) of the Au reflector is 80 nm. Figure 4(b-c) show the absorption distribution diagram which is defined by the absorbed optical power per unit volume (Pabs) due to material absorption in the Ge substrate under the Au-PMMA decoupler without or with Au reflector respectively [47,48], the position of z = 0 is the upper surface of the Ge substrate and x = 0 is the end of the waveguide. It is clear that after adding the Au reflector to the Ge substrate, most of the absorption is confined between the Au grating/Ge/Au reflector layer and the absorption is improved by an order of magnitude compared with the device without reflector added, which will facilitate the generation of carriers (electron-hole pairs and hot electrons) and enhance the photocurrent in practical devices [33,35,48,49]. It should be noted that in order to keep the same structure as the device without Au reflector as possible, we still use the Ge substrate for performance comparison as shown in Fig. 4(a). In fact, the substrate can be replaced by any other materials such as SiO2 when Au reflector is used (See Fig. S2 in Supplement 1).
Fig. 4. (a) Schematic diagram of the complete PIC with index matching layer and metal reflector in x-z plane. (b-c) Absorption distribution at the Au-PMMA grating decoupler of the PIC (b) without Au reflector and (c) with Au reflector calculated by the power analysis group as shown by the white dotted frame in Fig. 4(a) (T = 200 nm).
To further reveal the combined effects of the grating depth, index matching layer and metal reflector on the decoupling performance of the PIC devices, Fig. 5(a-d) shows the decoupling efficiency as a function of different grating depth in the 1100–1500 nm wavelength range of four different device structures. The decoupling efficiency is defined as the ratio of the normalized power flowing into the monitor (red dotted arrow in Fig. 4(a)) to the incident light, in this way, it is assumed that all photons flowing into the decoupling grating/Ge substrate interface will contribute to the generation of photocurrent which is convenient to compare the devices with different structures.
Fig. 5. (a-d) Decoupling efficiency as a function of different grating depth in the 1100–1500 nm wavelength range of four different device structures. (a) Basic Au-air device. (b) Basic Au-PMMA device. (c) Au-PMMA device with Au reflector. (d) Change the refractive index of the index matching layer in (c) from 1.5 (PMMA) to 1.565.
Figure 5(a-b) presents the decoupling efficiency of the basic Au-air and Au-PMMA devices without Au reflector at different grating depth. As mentioned above, although the SPPs couplers with these two structures can obtain the highest coupling efficiency when the grating depth is about 200–250 nm and 150–200 nm respectively, the grating depth to achieve the highest decoupling efficiency is reduced by about 50 nm because the large grating depth prevents the efficient scattering of photons into the substrate. So, the optimal operating points of the coupler and decoupler do not match. The mismatch can be significantly improved after using the Au reflector as shown in Fig. 5(c-d). Figure 5(c) is the decoupling efficiency of the Au-PMMA device with Au reflector which exhibits a double improvement over the basic Au-PMMA device and the optimal operating point returns to 200 nm. In this case the negative effect of the larger grating depth is fully compensated by the Au reflector, the coupling efficiency of the grating coupler dominates the final decoupling efficiency of the device. However, we noticed that the peak of the decoupling efficiency is shifted to around 1270 nm at this time and the decoupling efficiency is only 8% at the desired 1310 nm. To change the peak position, the traditional method is to change the period of the grating coupler, but we think it is difficult to actually fine-tune the grating period due to the fabrication error limitations and we also investigated the fabrication tolerance of the designed devices (See Fig. S4 in Supplement 1). According to Eq. (1), we try to adjust the refractive index of the index matching layer from 1.5 to 1.565 without changing any other structural parameters (P = 900 nm, W = 450 nm, p = 700 nm and w = 350 nm) as shown in Fig. 5(d). In this way, the maximum value (18%) of decoupling efficiency is stabilized around 1310 nm wavelength and 200 nm grating depth.
To explain the large increase in decoupling efficiency, Fig. 6(a) shows the normalized electric field distribution at the decoupler of the PIC with the n = 1.565 index matching layer but without Au reflector, at this time, most of the electric field is concentrated in the refractive index matching layer above the decoupling gratings with only a small amount of distribution in the Ge substrate. In Fig. 6(b), the Au reflector adding to the Ge substrate effectively enhances the electric field strength between the gratings and forms the localized plasmon resonance mode in the Ge layer between the gratings and reflector as shown by the white dotted frame in Fig. 6(b), which can greatly improve the scattering of SPPs and the light absorption in the Ge substrate. Due to the existence of the resonance mode, the Q-factor (λ/Δλ) of the decoupling spectrum of the optimized device is improved to about 15.3 compared with the basic Au-air device (See Fig. S4 in Supplement 1) [50–53]. The similar effect can be also seen in the grating coupler of the devices (See Fig. S3 & 4 in Supplement 1). It should be noted that the higher Q is important for some specific applications such as spectral resolution and refractive index detection because these applications require a narrow-band resonant peak [50–52]. Our devices actually need a wide-band response spectrum to meet wider wavelength application range and better wavelength jitter tolerance. Therefore, we do not pursue extremely high Q in our devices.
Fig. 6. (a-b) Normalized electric field distribution at the Au-(n = 1.565) grating decoupler of the PIC (a) without or (b) with bottom Au reflector (T = 200 nm, P = 900 nm, W = 450 nm, p = 700 nm and w = 350 nm).
Since the optimal operating point of the device can be effectively adjusted by changing the refractive index of the index matching layer as shown in Fig. 5(d), we consider whether continuous tunability of the operating point can be obtained by continuously changing the refractive index. Figure 7 shows the coupling (use the 1500 nm long power monitor as shown in Fig. 1(a)) and decoupling efficiency of the PIC with Au reflector and 200 nm grating depth when the refractive index of the index matching layer changes from 1.0 to 2.0. It is clear that the maximum value of coupling and decoupling efficiency of the PIC device changes almost linearly and synergistically from 1100 nm to 1500 nm when the refractive index is changed from 1.25 to 1.85 as shown by the red dotted arrow in Fig. 7. In addition, we can find the PIC device with the fixed structural parameters (T = 200 nm, P = 900 nm, W = 450 nm, p = 700 nm and w = 350 nm) has the best refractive index range (n ≈ 1.5∼1.65) and operating wavelength range (λ ≈ 1250∼1350 nm), in this range, the device can obtain more than 30% coupling efficiency with more than 12% decoupling efficiency. Although through some asymmetric structural designs, more than 50% coupling efficiency can be achieved [12], however, our designed device can avoid the additional etching process of these asymmetric structures, fully exploit the potential of the proposed simple structure, and the coupling efficiency of the final optimized device is increased to 38% which is much higher than the same type of SPPs grating coupler devices [27,28,33]. The dynamic change of refractive index in the range of 1.5–1.65 are feasible using suitable liquid crystal [37–39] or electro-optic materials [12,40]. In this case, it is possible to realize tunable PIC devices. In addition, similar to the phase drift compensation in the electronic devices, real-time adjustment of the refractive index offers a possible way to repair fabrication errors and correct for operating point drift in this PIC devices.
Fig. 7. (a) Coupling efficiency and (b) decoupling efficiency as a function of different refractive index of the index matching layer in the PIC with Au reflector (T = 200 nm, P = 900 nm, W = 450 nm, p = 700 nm and w = 350 nm).
4. Conclusion
In summary, we build an efficient and easily-fabricated PIC platform consisting periodic grating coupler, waveguide and grating decoupler. As a key component to realize SPPs excitation and coupling of the PIC device, we have clarified the optimal depth of coupling gratings through numerical simulation. By adding an index matching layer, the propagating SPPs field is better confined in the high index dielectric layer, which helps to increase the SPPs propagation distance and reduce the propagation loss. Furthermore, the efficient and tunable complete PIC device has been constructed under the dual action of index matching layer and Au reflector. We summarize the following benefits and potential applications: First, the Au reflector and index matching layer can greatly improve the SPPs coupling and decoupling efficiency of the device which helps to reduce the energy loss and improve the responsivity of the actual device; Second, the Au reflector greatly improves the SPPs utilization of the decoupler, compensates for the energy loss caused by the higher grating depth, unifies the optimal operating point of the SPPs coupler and the decoupler. Finally, the optimal operating point of the device can be adjusted linearly within a certain range by changing the refractive index of the matching layer which provides a possible solution for realizing tunable on-chip OEICs.
Funding
Postgraduate Research & Practice Innovation Program of Jiangsu Province (KYCX22_0227).
Disclosures
The authors declare no conflicts of interest.
Data availability
The data that support the findings of this study are available from the corresponding author upon reasonable request.
Supplemental document
See Supplement 1 for supporting content.
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